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Chapter 6: Problem 32

A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. How many sets of three marbles include all the yellow ones?

Short Answer

Expert verified
There are 8 possible sets of three marbles which include both yellow marbles.

Step by step solution

01

Identify given marbles and the ones needed to be picked

The given marbles in the bag are three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. We want to find how many sets of three marbles include all the yellow ones.
02

Count non-yellow marbles in the bag

Out of the total marbles, there are two yellow ones, so let's count the non-yellow marbles: 3 red marbles + 2 green marbles + 1 lavender marble + 2 orange marbles = 8 non-yellow marbles
03

Use counting principle to find combinations

To find the number of sets of three marbles that include both yellow marbles, we will consider choosing one of the 8 non-yellow marbles as the third marble in the set (since both yellow marbles are already included). There are 8 ways to choose the third marble in the set from the 8 non-yellow marbles.
04

Formulate the answer

There are 8 possible sets of three marbles which include both yellow marbles.

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